Proof of the Hodge Conjecture within the Unified Metabolic Causal Field

Key Points

• The aim is to provide a strict proof of the Hodge conjecture within a new mathematical framework.
• Utilized elements from holistic mathematics and inverse extremal limit theory
• Incorporated concepts from algebraic geometry such as Hodge structures and algebraic rings
• Employed category theory to unify the concepts within the causal field framework.
• Proved that every Hodge class is a rational linear combination of the generators of the algebraic ring.
• Showed strong explanatory power of holistic mathematics in addressing core problems in algebraic geometry.

Abstract